docs: silence background job output in shell integration snippet

[eni9889]

Summary

Tiny README tweak. The current shell integration snippet recommends:

if command -v claude-sync &> /dev/null; then
  claude-sync pull -q &
fi

In interactive zsh/bash, the trailing & causes the shell to print job-control messages every time a terminal is opened:

Last login: Mon May 11 21:18:11 on ttys009
[2] 17215
❯
[2]  + done       claude-sync pull -q
❯

These two extra lines per shell start are harmless but visually noisy — especially with a prompt that renders a separator line.

Fix

Wrap the background call in a subshell so the job is detached from the parent shell's job table:

(claude-sync pull -q &) >/dev/null 2>&1

The pull still runs in the background; the parent shell just never tracks it, so no [N] PID start line and no done completion line are printed. Redirecting stdout/stderr also keeps any stray output from leaking into the prompt.

Verified locally on macOS zsh 5.9 — terminal opens clean, claude-sync pull -q still runs (visible in ps).

Test plan

• Open a new interactive zsh/bash shell with the updated snippet — no [N] PID or + done lines appear
• Confirm claude-sync pull still executes (ps aux | grep claude-sync during shell start, or check sync state after)

[Copilot]

Pull request overview

Updates the README’s shell-integration snippet to avoid interactive job-control noise when claude-sync pull is launched in the background on shell startup.

Changes:

• Runs the background claude-sync pull -q inside a subshell and redirects output to suppress job-control messages and stray output.
• Adds an explanatory note describing why the subshell pattern is used.

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